Efficient Sampling Algorithms for Approximate Temporal Motif Counting (Extended Version)

TL;DR

This paper introduces efficient approximate algorithms for counting temporal motifs in large temporal graphs, leveraging random sampling techniques to improve performance and scalability over existing methods.

Contribution

It proposes a generic edge sampling algorithm and an improved hybrid EWS algorithm for counting temporal motifs, with theoretical analysis and extensive experimental validation.

Findings

Higher efficiency compared to state-of-the-art methods

Better accuracy in motif counting

Greater scalability on real-world datasets

Abstract

A great variety of complex systems ranging from user interactions in communication networks to transactions in financial markets can be modeled as temporal graphs, which consist of a set of vertices and a series of timestamped and directed edges. Temporal motifs in temporal graphs are generalized from subgraph patterns in static graphs which take into account edge orderings and durations in addition to structures. Counting the number of occurrences of temporal motifs is a fundamental problem for temporal network analysis. However, existing methods either cannot support temporal motifs or suffer from performance issues. In this paper, we focus on approximate temporal motif counting via random sampling. We first propose a generic edge sampling (ES) algorithm for estimating the number of instances of any temporal motif. Furthermore, we devise an improved EWS algorithm that hybridizes edge sampling with wedge sampling for counting temporal motifs with 3 vertices and 3 edges. We provide comprehensive analyses of the theoretical bounds and complexities of our proposed algorithms. Finally, we conduct extensive experiments on several real-world datasets, and the results show that our ES and EWS algorithms have higher efficiency, better accuracy, and greater scalability than the state-of-the-art sampling method for temporal motif counting.